Speaker: Alen Alexanderian
Abstract. Mathematical models of physical phenomena often include parameters which are hard or impossible to measure accurately and are thus considered uncertain. The emerging field of uncertainty quantification provides a framework for quantifying such model uncertainties and enables predictions with quantified and potentially reduced uncertainty. In general, modeling under uncertainty encompasses forward modeling and uncertainty propagation, inverse modeling and statistical inference, as well as optimal design of experiments. I will focus on recent advances in numerical methods for infinite-dimensional Bayesian inverse problems and optimal experimental design (OED) under uncertainty. The driving applications are those of inferring field quantities in mathematical models governed by PDEs. These problems are computationally challenging due to expensive forward solves, large parameter dimension, and the need for consistent discretizations. I will also discuss spectral methods for uncertainty quantification with applications to ocean general circulation modeling under uncertainty, and stochastic chemical kinetics.